id
int64 -30,985
55.9k
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stringlengths 5
437k
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|---|---|
12,742 |
9/10 \cdot 5 + b = 5 rightarrow b = 5 - \frac12 \cdot 9 = 1/2
|
53,726 |
U = \left[x, y\right] \Rightarrow ( \begin{array}{cc}x * x * x & y*x^2\\x*y*x & x*y^2\end{array}, \begin{pmatrix}x^2*y & y*x*y\\x*y^2 & y * y^2\end{pmatrix}) = U * U^2
|
11,857 |
4 = \left((-1) + 3^2\right)/2
|
12,222 |
y + (-1) = t \Rightarrow 1 + t = y
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-25,230 |
1.5\cdot \sqrt{16} = 1.5\cdot 4 = 6
|
-3,862 |
\tfrac{x^4}{x} = \dfrac{x}{x}xx x = x^3
|
36,020 |
\frac{15}{15 + 2 + 7} = \frac{15}{24}
|
21,879 |
(-1 + \sqrt{-3})/2 = -\frac{1}{2} + \frac{\sqrt{3}*\text{i}}{2}
|
9,460 |
\operatorname{acos}(-x) = \operatorname{acos}(\cos(-\operatorname{acos}\left(x\right) + \pi)) \Rightarrow \pi - \operatorname{acos}(x) = \operatorname{acos}(-x)
|
22,844 |
-q^2 + t \cdot t = (t + q) (-q + t)
|
23,613 |
{m + \left(-1\right) \choose \left(-1\right) + m} + {(-1) + m \choose m} = {m \choose m}
|
-2,847 |
\sqrt{4}\cdot \sqrt{3} + \sqrt{3} = \sqrt{3} + 2\cdot \sqrt{3}
|
-26,542 |
100 - z \cdot z\cdot 9 = (10 + 3\cdot z)\cdot (-3\cdot z + 10)
|
24,048 |
(x^2 + y^2) \cdot (x^2 + y^2) = x^4 + x^2 \cdot y \cdot y + y^4 + x^2 \cdot y^2 = x^2 + x^2 \cdot y^2
|
-11,662 |
9 = 81^{1/2}
|
54,321 |
\frac{1}{2 \cdot t} \cdot \left(n^{1/2} + t \cdot a\right) = a + \frac{1}{2 \cdot t} \cdot (n^{1/2} + t \cdot a) - a = a + \tfrac{1}{2 \cdot t} \cdot (n^{1/2} + t \cdot a - 2 \cdot t \cdot a) = a + \frac{1}{2 \cdot t} \cdot (n^{1/2} - t \cdot a)
|
18,983 |
\frac{1}{h*d}*(z*d + y*h) = \frac{z}{h} + y/d
|
19,594 |
a^2 \cdot a - b \cdot b \cdot b = (b^2 + a^2 + a\cdot b)\cdot (-b + a)
|
-20,632 |
\dfrac{1}{9 \cdot t} \cdot 9 \cdot t \cdot (-3/8) = \tfrac{t \cdot (-27)}{72 \cdot t}
|
6,252 |
-\sin\left(X\right) = \cos\left(X + \pi/2\right)
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19,386 |
1 + 3*z_1 = z_2 \Rightarrow z_1 = \frac{1}{3}*(z_2 + (-1))
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-20,069 |
\frac{3}{3} \cdot \frac{5 \cdot z}{8 \cdot z + 9} = \frac{z}{24 \cdot z + 27} \cdot 15
|
5,344 |
\sin^2\left(y\right) = \frac12*(1 - \cos(2*y))
|
6,153 |
\left(y + 1\right) y\cdot \left(y + (-1)\right) = -y + y \cdot y^2
|
4,315 |
\mathbb{E}[\frac{Z}{Y}] = \frac{\mathbb{E}[Z]}{\mathbb{E}[Y]}
|
41,813 |
\frac{-\tan^2{\frac{y}{2}} + 1}{\tan^2{y/2} + 1} = \cos{y}
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-20,041 |
\frac{3\cdot t + 2}{3\cdot t + 2}\cdot \left(-9/5\right) = \frac{1}{10 + t\cdot 15}\cdot (-27\cdot t + 18\cdot (-1))
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17,088 |
y^{y + (-1)}*y = y^y
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-10,359 |
\frac{1}{x \cdot 15 + 30}(x \cdot 15 + 30 \left(-1\right)) = 5/5 \frac{6\left(-1\right) + x \cdot 3}{6 + x \cdot 3}
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35,804 |
\binom{7}{3} = \frac{7!}{3! \cdot \left(7 + 3 \cdot (-1)\right)!} = 35
|
17,640 |
x \cdot x = (100 \cdot h \cdot x)^2 = 10000 \cdot h \cdot x^2
|
9,005 |
(2a-4b)=-2(2b-a)
|
16,588 |
\left(2 + 3\cdot j\right)\cdot 2 = 4 + 6\cdot j
|
4,358 |
(2 \cdot (-1) + l)! \cdot l \cdot l = l! + (2 \cdot (-1) + l)! + (l + (-1))!
|
16,385 |
\sin{a} \cdot \cos{a} = \sin{2 \cdot a}/2
|
-8,480 |
\left(-9\right) \cdot (-1) = 9
|
9,081 |
3! \cdot \binom{5}{3} \cdot \binom{5}{3} \cdot 2 = 1200
|
42,936 |
6^{50} = (6^2)^{25} = 36^{25} = 7^{25}
|
25,657 |
-10 = 3 \cdot (-1) + 2 + 5 \cdot (-1) + 4 \cdot (-1)
|
-22,312 |
n^2 + 10 n + 16 = (8 + n) (2 + n)
|
-8,010 |
\frac{1}{2 - i*5}*(-12 + i) = \tfrac{i*5 + 2}{2 + 5*i}*\frac{1}{2 - 5*i}*(i - 12)
|
6,051 |
(z - y) \cdot \left(z^{k + (-1)} + z^{k + 2 \cdot (-1)} \cdot y + \dotsm + z \cdot y^{k + 2 \cdot (-1)} + y^{(-1) + k}\right) = -y^k + z^k
|
12,489 |
\pi/12*\left(2 n + 1\right) = \dfrac{1}{12} \pi + n \pi/6
|
-11,622 |
i*8 + 3 + 5\left(-1\right) = i*8 - 2
|
8,665 |
v\times \frac{\mathrm{d}w}{\mathrm{d}x} + w\times \frac{\mathrm{d}v}{\mathrm{d}x} = \frac{\partial}{\partial x} (v\times w)
|
27,579 |
G^2 + G + 1 = (G^2 + 1)/2 + \frac12*(G + 1)^2 \geq \dfrac12*(G^2 + 1)
|
29,193 |
(g_1 \cdot 2)^2 - (2 \cdot g_2)^2 \cdot n = 4 \cdot (g_1 \cdot g_1 - g_2^2 \cdot n)
|
25,197 |
\dfrac{1}{x^2 + y^2 + z^2} = \frac{1}{z^2 + x^2 + y \cdot y}
|
6,730 |
c^{h_2}\cdot c^{h_1} = c^{h_1 + h_2}
|
5,995 |
a'^2\cdot 4 - 10\cdot \left(x^2\cdot 4 + 4\cdot x + 1\right) = 4\cdot (-10\cdot x + a'^2 \pm x^2\cdot 10) + 10\cdot (-1)
|
18,787 |
3*\left(-1\right) + S*3 \geq 0 \Rightarrow S \geq 1
|
-4,609 |
\dfrac{8 \cdot x + 32}{x \cdot x + 8 \cdot x + 15} = \frac{4}{5 + x} + \frac{4}{3 + x}
|
20,894 |
\sin{x} = \frac{Y}{q} \Rightarrow \sin{x}\times q = Y
|
-11,232 |
(z + g)^2 = (z + g) \cdot \left(z + g\right) = z^2 + 2 \cdot g \cdot z + g^2
|
20,482 |
2 \cdot (a^2 + c \cdot c) = (a + c) \cdot (a + c) + (a - c) \cdot (a - c) \geq (a + c)^2
|
21,670 |
0 = \mathbb{E}[V]\Longrightarrow \mathbb{E}[V^2] = 0
|
7,673 |
-G = G \Rightarrow G\cdot 2 = 0
|
17,640 |
m^2 = (100 \cdot x \cdot m) \cdot (100 \cdot x \cdot m) = 10000 \cdot x \cdot m^2
|
-21,035 |
\frac{a + 6\cdot (-1)}{4\cdot \left(-1\right) - 5\cdot a}\cdot \frac77 = \frac{7\cdot a + 42\cdot (-1)}{-a\cdot 35 + 28\cdot (-1)}
|
38,957 |
10 \left(-1\right) + 10 + 10 = 10
|
21,080 |
3\cdot \epsilon + \epsilon\cdot 3 = 6\cdot \epsilon
|
11,971 |
\frac{d}{du} (\frac{1}{e^u}e^u) = 0 = e^u - e^{2u}
|
-22,773 |
7\cdot 3/(7\cdot 8) = \frac{21}{56}
|
9,458 |
\frac{1}{1 + \frac{1}{2\cdot 3 - x \cdot x + \dots}\cdot x^2}\cdot x = \sin{x}
|
42 |
-90 x \cdot x = -x^2 \cdot \left(30 (-1) + 6 \cdot 20\right)
|
21,950 |
1 = \arccos\left(\cos(1)\right)
|
41,331 |
2*7 + 13*\left(-1\right) = 1
|
6,827 |
V = \pi r^2 h\Longrightarrow h = \frac{1}{\pi r^2} V
|
23,490 |
x\times a = b\Longrightarrow \frac1a\times b = x
|
15,189 |
4(1 + y + x) = xy \implies 20 = (y + 4(-1)) (4(-1) + x)
|
2,758 |
2\pi x = 2i\pi\Longrightarrow x = i
|
2,688 |
3\frac{y}{9} = y/3
|
5,131 |
\cos{\theta} = y/r\Longrightarrow y = \cos{\theta} r
|
35,450 |
\int |h|\,\mathrm{d}x = \int |h|\,\mathrm{d}x
|
55,611 |
6 = 1 + 2 + 1 + 2
|
39,385 |
4 = \frac{1}{4}16
|
16 |
p = p + (1 - p) \cdot 0
|
17,331 |
x^4 - 7x^2 + 1 = \left(x^2 + 1\right)^2 - 9x * x = \left(x * x + 1 + 3x\right) (x^2 + 1 - 3x)
|
-19,731 |
\frac{49}{9}1 = \frac{1}{9}49
|
20,930 |
3^{1/2} + 2 = \tan{\pi \cdot 5/12}
|
-188 |
\frac{8!}{\left(8 + 3*\left(-1\right)\right)!*3!} = {8 \choose 3}
|
18,900 |
2 = \dfrac{1}{2} \cdot (e^x - e^{-x}) \implies 4 = e^x - e^{-x}
|
29,806 |
4^2 + 4^3 + ... + 4^k + 4^{k + 1} = \left(4^k + (-1)\right) \cdot 4^2/3
|
3,567 |
b' a' + 1 = (b' + a') \cdot 2
|
29,779 |
\dfrac{6*5*4}{6^3} = 5/9
|
-9,808 |
-0.45 = -\frac{1}{10} 4 = -\dfrac{9}{20}
|
-744 |
\left(e^{7 \cdot i \cdot \pi/12}\right)^{13} = e^{\frac{1}{12} \cdot 7 \cdot \pi \cdot i \cdot 13}
|
8,164 |
X = (1 + 0 \times (-1)) \times X
|
-6,998 |
\frac27 = 4/7\cdot 3/6
|
10,356 |
\left(C \cdot 3 = \frac1C\Longrightarrow x = 3C^2\right)\Longrightarrow \frac{x}{3} = C^2
|
28,535 |
d^{m + 1} = d^1\cdot d^m
|
-27,714 |
\frac{\mathrm{d}}{\mathrm{d}x} (-\cos{x} \times 10) = \sin{x} \times 10
|
-12,014 |
7/8 = s/(6 \pi)*6 \pi = s
|
-9,327 |
-8 \cdot p + 24 \cdot (-1) = -2 \cdot 2 \cdot 2 \cdot p - 2 \cdot 2 \cdot 2 \cdot 3
|
-5,021 |
10^1*18.0 = 10^{6 - 5}*18.0
|
10,735 |
1/18 + \frac12 + 1/3 + \tfrac{1}{9} = 1
|
25,472 |
\pi^{\frac{1}{2}}/(1/2)! = 2
|
17,837 |
\frac13 \left(\frac{1}{y + (-1)} - \frac{1}{y^2 + y + 1} (y + 2)\right) = \frac{1}{y^3 + \left(-1\right)}
|
27,092 |
x^2 = z \Rightarrow \frac{dz}{dx} = 2\times x
|
-23,580 |
\frac{\dfrac{5}{7}}{5}\cdot 1 = 1/7
|
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